What is the solution for 4*(d^2y)/(dx^2)+12*(dy)/(dx)+9y=0 ?

The solution for 4*(d^2y)/(dx^2)+12*(dy)/(dx)+9y=0 is y=c_{1}e^{-(3x)/2}+c_{2}e^{-(3x)/2}x

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4(d^2y)/(dx^2)+12(dy)/(dx)+9y=0

4 \cdot \frac{d ^{2} y}{d x ^{2}} + 12 \cdot \frac{d y}{d x} + 9 y = 0

y = c_{1} e^{- \frac{3 x}{2}} + c_{2} e^{- \frac{3 x}{2}} x

Solution steps

4 \cdot \frac{d ^{2} y}{d x ^{2}} + 12 \cdot \frac{d y}{d x} + 9 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{3 x}{2}} + c_{2} e^{- \frac{3 x}{2}} x

y = c_{1} e^{- \frac{3 x}{2}} + c_{2} e^{- \frac{3 x}{2}} x

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = \frac{2}{3}

0.2 q^{^{''}} + 4 q^{^{'}} + 100 q = 0

y^{^{''}} - 20 y^{^{'}} + 100 y = 0, y (0) = 4, y (1) = 3

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 10 y = 0

y^{^{''}} + 8 y^{^{'}} - 2 y = 0

What is the solution for 4*(d^2y)/(dx^2)+12*(dy)/(dx)+9y=0 ?
The solution for 4*(d^2y)/(dx^2)+12*(dy)/(dx)+9y=0 is y=c_{1}e^{-(3x)/2}+c_{2}e^{-(3x)/2}x